B/rnumt: Real Number Template.
 
@Purpose: Support for real numbers.
 
@-------------------------------------------------------------------------------

@p Printing reals.
Most of the code in this section is by Andrew Plotkin, and derives from test
cases used to check the floating-point extensions to Glulx.

@c
#Ifdef TARGET_GLULX;

[ REAL_NUMBER_TY_Say fp;
	print (Float) fp;
];

[ REAL_NUMBER_TY_Compare r1 r2;
	@jflt r1 r2 ?less;
	@jfeq r1 r2 0 ?same;
	return 1;
	.same; return 0;
	.less; return -1;
];

[ NUMBER_TY_to_REAL_NUMBER_TY int real; @numtof int real; return real; ];
[ REAL_NUMBER_TY_to_NUMBER_TY real int; @ftonumn real int; return int; ];

[ REAL_NUMBER_TY_Sin in out; @sin in out; return out; ];
[ REAL_NUMBER_TY_Cos in out; @cos in out; return out; ];
[ REAL_NUMBER_TY_Tan in out; @tan in out; return out; ];
[ REAL_NUMBER_TY_Arcsin in out; @asin in out; return out; ];
[ REAL_NUMBER_TY_Arccos in out; @acos in out; return out; ];
[ REAL_NUMBER_TY_Arctan in out; @atan in out; return out; ];

[ REAL_NUMBER_TY_Sinh in tmp out;
	@exp in tmp;
	@fsub M_0 in in;
	@exp in out;
	@fadd tmp out out;
	@fmul out M_HALF out;
	return out;
];

[ REAL_NUMBER_TY_Cosh in tmp out;
	@exp in tmp;
	@fsub M_0 in in;
	@exp in out;
	@fsub tmp out out;
	@fmul out M_HALF out;
	return out;
];

[ REAL_NUMBER_TY_Tanh in tmp out;
	tmp = REAL_NUMBER_TY_Sinh(in);
	in = REAL_NUMBER_TY_Cosh(in);
	@fdiv tmp in out;
	return out;
];

[ REAL_NUMBER_TY_Reciprocal in out; @fdiv M_1 in out; return out; ];
[ REAL_NUMBER_TY_Negate in out; @fsub M_0 in out; return out; ];
[ REAL_NUMBER_TY_Plus x y out; @fadd x y out; return out; ];
[ REAL_NUMBER_TY_Minus x y out; @fsub x y out; return out; ];
[ REAL_NUMBER_TY_Times x y out; @fmul x y out; return out; ];
[ REAL_NUMBER_TY_Divide x y out; @fdiv x y out; return out; ];
[ REAL_NUMBER_TY_Remainder x y r q; @fmod x y r q; return r; ];
[ REAL_NUMBER_TY_Approximate x y quotient out;
	@fdiv x y quotient;
	@fadd quotient M_HALF quotient;
	@floor quotient quotient;
	@fmul quotient y out;
	return out;
];
[ REAL_NUMBER_TY_Root x out; @sqrt x out; return out; ];
[ REAL_NUMBER_TY_Cube_Root x out; @pow x M_THIRD out; return out; ];
[ REAL_NUMBER_TY_Pow x y out; @pow x y out; return out; ];
[ REAL_NUMBER_TY_Exp x out; @exp x out; return out; ];
[ REAL_NUMBER_TY_Log x out; @log x out; return out; ];
[ REAL_NUMBER_TY_BLog x n d out;
	@log x out;
	if (n == 10) d = M_LOG10;
	else {
		@numtof n d;
		@log d d;
	}
	@fdiv out d out;
	return out;
];
[ REAL_NUMBER_TY_Floor x out; @floor x out; return out; ];
[ REAL_NUMBER_TY_Ceiling x out; @ceil x out; return out; ];
[ REAL_NUMBER_TY_Abs x; return x & $7fffffff; ];
[ REAL_NUMBER_TY_Nan x; @jisnan x ?Nan; rfalse; .Nan; rtrue; ];

Constant M_0    = $0;
Constant M_1    = $3F800000;
Constant M_HALF = $3F000000; ! 1/3
Constant M_THIRD = $3EAAAAAB; ! 1/3
Constant M_LOG10 = $40135D8E; ! log(10)
Constant M_N1   = $BF800000; ! -1
Constant M_PI   = $40490FDB;
Constant M_NPI  = $C0490FDB;
Constant M_2PI  = $40C90FDB; ! 2*pi
Constant M_PI2  = $3FC90FDB; ! pi/2
Constant M_NPI2 = $BFC90FDB; 
Constant M_E    = $402DF854;
Constant M_E2   = $40EC7326; ! e^2
Constant M_N0   = $80000000; ! negative zero
Constant M_INF  = $7F800000; ! infinity
Constant M_NINF = $FF800000; ! negative infinity
Constant M_NAN  = $7F800001; ! one of many NaN values
Constant M_NNAN = $FF800001; ! another, with a sign bit

! Floating-point parsing routines.

! Parse a float from a text buffer. Returns a float value, or FLOAT_NAN if
! no value was understood.
!
! The recognized format, if you'll pardon a slightly bastardized regexp
! syntax, is "S?D*(PD*)?(ES?D+)?" where S is a sign character "+" or "-",
! D is a decimal digit "0" to "9", P is a decimal point ".",
! and E is the exponential modifier "E" or "e".
!
! For flexibility, the string "M10^" is also accepted for E, where M is
! "X", "x", "*", or the multiplication sign @{D7}. Optional spaces are
! allowed before and after the M sign. (But only for the "10^" form of
! the exponent, not the "e" form.)
!
! This routine does not try to recognize special names for infinity or NaN,
! but it can return FLOAT_INFINITY or FLOAT_NINFINITY if the exponent is too
! large.
!
! This routine relies on floating-point math. Therefore, the same string
! may parse to slightly different float values on different interpreters!
! Be warned.
!
! If useall is true, this insists on using all len characters from the buffer.
! (It returns FLOAT_NAN if any unrecognized characters are left over.)
! Contrariwise, if useall is false, unused characters at the end of the buffer
! are fine. (But not at the beginning; the float must start at the beginning
! of the buffer.)
! 
[ FloatParse buf len useall
	res ix val ch ten negative intpart fracpart fracdiv
	expon expnegative count;
	
!	print "FloatParse <";
!	for (ix=0: ix<len: ix++) print (char) buf->ix;
!	print ">^";

	if (len == 0)
		return FLOAT_NAN;
		
	ix = 0;
	negative = false;
	intpart = 0;
	fracpart = 0;
	@numtof 10 ten;

	! Sign character (optional)
	ch = buf->ix;
	if (ch == '-') {
		negative = true;
		ix++;
	}
	else if (ch == '+') {
		ix++;
	}

	! Some digits (optional)
	for (count=0 : ix<len : ix++, count++) {
		ch = buf->ix;
		if (ch < '0' || ch > '9')
			break;
		val = (ch - '0');
		@numtof val val;
		@fmul intpart ten intpart;
		@fadd intpart val intpart;
	}

	! Decimal point and more digits (optional)
	if (ix<len && buf->ix == '.') {
		ix++;
		@numtof 1 fracdiv;
		for ( : ix<len : ix++, count++) {
			ch = buf->ix;
			if (ch < '0' || ch > '9')
				break;
			val = (ch - '0');
			@numtof	val val;
			@fmul fracpart ten fracpart;
			@fadd fracpart val fracpart;
			@fmul fracdiv ten fracdiv;
		}
		@fdiv fracpart fracdiv fracpart;
	}

	! If there are no digits before *or* after the decimal point, fail.
	if (count == 0)
		return FLOAT_NAN;

	! Combine the integer and fractional parts.
	@fadd intpart fracpart res;

	! Exponent (optional)
	if (ix<len && buf->ix == 'e' or 'E' or ' ' or '*' or 'x' or 'X' or $D7) {
		if (buf->ix == 'e' or 'E') {
			! no spaces, just the 'e'
			ix++;
			if (ix == len)
				return FLOAT_NAN;
		}
		else {
			! any number of spaces, "*", any number of spaces more, "10^"
			while (ix < len && buf->ix == ' ')
				ix++;
			if (ix == len)
				return FLOAT_NAN;
			if (buf->ix ~= '*' or 'x' or 'X' or $D7)
				return FLOAT_NAN;
			ix++;
			while (ix < len && buf->ix == ' ')
				ix++;
			if (ix == len)
				return FLOAT_NAN;
			if (buf->ix ~= '1')
				return FLOAT_NAN;
			ix++;
			if (buf->ix ~= '0')
				return FLOAT_NAN;
			ix++;
			if (buf->ix ~= $5E)
				return FLOAT_NAN;
			ix++;
		}

		! Sign character (optional)
		expnegative = false;
		ch = buf->ix;
		if (ch == '-') {
			expnegative = true;
			ix++;
		}
		else if (ch == '+') {
			ix++;
		}

		expon = 0;
		! Some digits (mandatory)
		for (count=0 : ix<len : ix++, count++) {
			ch = buf->ix;
			if (ch < '0' || ch > '9')
				break;
			expon = 10*expon + (ch - '0');
		}

		if (count == 0)
			return FLOAT_NAN;

		if (expnegative)
			expon = -expon;

		if (expon) {
			@numtof expon expon;
			@pow ten expon val;
			@fmul res val res;
		}
	}

	if (negative) {
		! set the value's sign bit
		res = $80000000 | res;
	}

	if (useall && ix ~= len)
		return FLOAT_NAN;
	return res;
];

! An I6 grammar routine (GPR) for floats. On success, this returns
! GPR_NUMBER and stores a value in the global parsed_number.
!
! This is quite a nuisance, actually, because "." is a word separator.
! Also, we want to accept command sequences like "type 4. look"! So we
! need to collect a set of words made up of digits, signs, periods, and
! the letter "e", but without any intervening whitespace, and excluding
! a trailing period.
!
! (This will fail to correctly parse "type 4.e", but I think that is a
! small flaw. A player would more likely try "type 4. e" or, really,
! not concatenate commands at all. It will also parse "type 4. on keyboard"
! as two commands, even though "4." is a legitimate float literal.
! Contrariwise, "type 4. x me" will be taken as one command. (Because the "x"
! *could* be a continuation of the float, and I don't back up when it turns
! out not to be.) I don't plan to worry about these cases.)

[ FLOAT_TOKEN buf bufend ix ch firstwd newstart newlen lastchar lastwasdot;
	if (wn > num_words)
		return GPR_FAIL;

	! We're going to collect a set of words. Start with zero words.
	firstwd = wn;
	buf = WordAddress(wn);
	bufend = buf;
	lastchar = 0;

	while (wn <= num_words) {
		newstart = WordAddress(wn);
		if (newstart ~= bufend) {
			! There's whitespace between the previous word and this one.
			! Whitespace is okay around an asterisk...
			if ((lastchar ~= '*' or 'x' or 'X' or $D7)
				&& (newstart->0 ~= '*' or 'x' or 'X' or $D7)) {
				! But around any other character, it's not.
				! Don't include the new word.
				break;
			}
		}
		newlen = WordLength(wn);
		for (ix=0 : ix<newlen : ix++) {
			ch = newstart->ix;
			if (~~((ch >= '0' && ch <= '9')
				|| (ch == '-' or '+' or 'E' or 'e' or '.' or 'x' or 'X' or '*' or $D7 or $5E)))
				break;
		}
		if (ix < newlen) {
			! This word contains an invalid character.
			! Don't include the new word.
			break;
		}
		! Okay, include it.
		bufend = newstart + newlen;
		wn++;
		lastchar = (bufend-1)->0;
		lastwasdot = (newlen == 1 && lastchar == '.');
	}

	if (wn > firstwd && lastwasdot) {
		! Exclude a trailing period.
		wn--;
		bufend--;
	}

	if (wn == firstwd) {
		! No words accepted.
		return GPR_FAIL;
	}

	parsed_number = FloatParse(buf, bufend-buf, true);
	if (parsed_number == FLOAT_NAN)
		return GPR_FAIL;
	return GPR_NUMBER;
];

! Floating-point printing routines. (These are based on code in
! Glulxercise.inf, but modified.)
  
! Print a float. This uses exponential notation ("[-]N.NNNe[+-]NN") if
! the exponent is not between 6 and -4. If it is (that is, if the
! absolute value is near 1.0) then it uses decimal notation ("[-]NNN.NNNNN").
! The precision is the number of digits after the decimal point
! (at least one, no more than eight). The default is five, because
! beyond that rounding errors creep in, and even exactly-represented
! float values are printed with trailing fudgy digits.
! Trailing zeroes are trimmed.
[ Float val prec   pval;
	pval = val & $7FFFFFFF;

	@jz pval ?UseFloatDec;
	@jfge pval $49742400 ?UseFloatExp; ! 1000000.0
	@jflt pval $38D1B717 ?UseFloatExp; ! 0.0001

	.UseFloatDec;
	return FloatDec(val, prec);
	.UseFloatExp;
	return FloatExp(val, prec);
];

Array PowersOfTen --> 1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000;

! Print a float in exponential notation: "[-]N.NNNe[+-]NN".
! The precision is the number of digits after the decimal point
! (at least one, no more than eight). The default is five, because
! beyond that rounding errors creep in, and even exactly-represented
! float values are printed with trailing fudgy digits.
! Trailing zeroes are trimmed.
[ FloatExp val prec   log10val expo fexpo idig ix pow10;
	if (prec == 0)
		prec = 5;
	if (prec > 8)
		prec = 8;
	pow10 = PowersOfTen --> prec;

	! Knock off the sign bit first.
	if (val & $80000000) {
		@streamchar '-';
		val = val & $7FFFFFFF;
	}
	
	@jisnan val ?IsNan;
	@jisinf val ?IsInf;

	if (val == $0) {
		expo = 0;
		idig = 0;
		jump DoPrint;
	}

	! Take as an example val=123.5, with precision=6. The desired
	! result is "1.23000e+02".
	
	@log val sp;
	@fdiv sp $40135D8E log10val; ! $40135D8E is log(10)
	@floor log10val fexpo;
	@ftonumn fexpo expo;
	! expo is now the exponent (as an integer). For our example, expo=2.

	@fsub log10val fexpo sp;
	@numtof prec sp;
	@fadd sp sp sp;
	@fmul sp $40135D8E sp;
	@exp sp sp;
	! The stack value is now exp((log10val - fexpo + prec) * log(10)).
	! We've shifted the decimal point left by expo digits (so that
	! it's after the first nonzero digit), and then right by prec
	! digits. In our example, that would be 1235000.0.
	@ftonumn sp idig;
	! Round to an integer, and we have 1235000. Notice that this is
	! exactly the digits we want to print (if we stick a decimal point
	! after the first).

	.DoPrint;
	
	if (idig >= 10*pow10) {
		! Rounding errors have left us outside the decimal range of
		! [1.0, 10.0) where we should be. Adjust to the next higher
		! exponent.
		expo++;
		@div idig 10 idig;
	}
	
	! Trim off trailing zeroes, as long as there's at least one digit
	! after the decimal point. (Delete this stanza if you want to
	! keep the trailing zeroes.)
	while (prec > 1) {
		@mod idig 10 sp;
		@jnz sp ?DoneTrimming;
		@div pow10 10 pow10;
		@div idig 10 idig;
		prec--;
	}
	.DoneTrimming;
	
	for (ix=0 : ix<=prec : ix++) {
		@div idig pow10 sp;
		@mod sp 10 sp;
		@streamnum sp;
		if (ix == 0)
			@streamchar '.';
		@div pow10 10 pow10;
	}

	! Print the exponent. There are two conventions coded here: the
	! programmatic ("1.0e+00") and the literary ("1.0 x 10^0").
	#ifndef FLOAT_PROGRAMMING_EXPONENTS;
		PrintMultiplicationSign();
		@streamstr "10";
		@streamchar $5E;
		@streamnum expo;
	#ifnot;
		! Convention is to use at least two digits.
		@streamchar 'e';
		if (expo < 0) {
			@streamchar '-';
			@neg expo expo;
		}
		else {
			@streamchar '+';
		}
		if (expo < 10)
			@streamchar '0';
		@streamnum expo;
	#endif; ! FLOAT_PROGRAMMING_EXPONENTS
	
	rtrue;

	.IsNan;
	PrintNan();
	rtrue;

	.IsInf;
	PrintInfinity();
	rtrue;
];

! Print a float in decimal notation: "[-]NNN.NNNNN".
! The precision is the number of digits after the decimal point
! (at least one, no more than eight). The default is five, because
! beyond that rounding errors creep in, and even exactly-represented
! float values are printed with trailing fudgy digits.
! Trailing zeroes are trimmed.
[ FloatDec val prec   log10val int fint extra0 frac idig ix pow10;
	if (prec == 0)
		prec = 5;
	if (prec > 8)
		prec = 8;
	pow10 = PowersOfTen --> prec;
	
	! Knock off the sign bit first.
	if (val & $80000000) {
		@streamchar '-';
		val = val & $7FFFFFFF;
	}
	
	@jisnan val ?IsNan;
	@jisinf val ?IsInf;

	! Take as an example val=123.5, with precision=6. The desired result
	! is "123.50000".
	
	extra0 = 0;
	@fmod val $3F800000 frac fint; ! $3F800000 is 1.0.
	@ftonumz fint int;
	! This converts the integer part of the value to an integer value;
	! in our example, 123.
	
	if (int == $7FFFFFFF) {
		! Looks like the integer part of the value is bigger than
		! we can store in an int variable. (It could be as large
		! as 3e+38.) We're going to have to use a log function to
		! reduce it by some number of factors of 10, and then pad
		! with zeroes.
		@log fint sp;
		@fdiv sp $40135D8E log10val; ! $40135D8E is log(10)
		@ftonumz log10val extra0;
		@sub extra0 8 extra0;
		! extra0 is the number of zeroes we'll be padding with.
		@numtof extra0 sp;
		@fsub log10val sp sp;
		@fmul sp $40135D8E sp;
		@exp sp sp;
		! The stack value is now exp((log10val - extra0) * log(10)).
		! We've shifted the decimal point far enough left to leave
		! about eight digits, which is all we can print as an integer.
		@ftonumz sp int;
	}

	! Print the integer part.
	@streamnum int;
	for (ix=0 : ix<extra0 : ix++)
		@streamchar '0';

	@streamchar '.';

	! Now we need to print the frac part, which is .5.
	
	@log frac sp;
	@fdiv sp $40135D8E log10val; ! $40135D8E is log(10)
	@numtof prec sp;
	@fadd log10val sp sp;
	@fmul sp $40135D8E sp;
	@exp sp sp;
	! The stack value is now exp((frac + prec) * log(10)).
	! We've shifted the decimal point right by prec
	! digits. In our example, that would be 50000.0.
	@ftonumn sp idig;
	! Round to an integer, and we have 50000. Notice that this is
	! exactly the (post-decimal-point) digits we want to print.

	.DoPrint;
	
	if (idig >= pow10) {
		! Rounding errors have left us outside the decimal range of
		! [0.0, 1.0) where we should be. I'm not sure this is possible,
		! actually, but we'll just adjust downward.
		idig = pow10 - 1;
	}

	! Trim off trailing zeroes, as long as there's at least one digit
	! after the decimal point. (Delete this stanza if you want to
	! keep the trailing zeroes.)
	while (prec > 1) {
		@mod idig 10 sp;
		@jnz sp ?DoneTrimming;
		@div pow10 10 pow10;
		@div idig 10 idig;
		prec--;
	}
	.DoneTrimming;
	
	@div pow10 10 pow10;
	for (ix=0 : ix<prec : ix++) {
		@div idig pow10 sp;
		@mod sp 10 sp;
		@streamnum sp;
		@div pow10 10 pow10;
	}
	rtrue;

	.IsNan;
	PrintNan();
	rtrue;

	.IsInf;
	PrintInfinity();
	rtrue;
];

[ PrintInfinity;
	@streamunichar $221E;
	! @streamstr "Inf";
];

[ PrintNan;
	@streamunichar $26a0;
	! @streamstr "NaN";
];

[ PrintMultiplicationSign;
	print " ";
	@streamunichar $D7;
	print " ";
	! @streamstr " x ";
];

#Ifnot; ! TARGET_GLULX

[ REAL_NUMBER_TY_Say real; print real; ]; ! Needs to exist, but likely never used

[ REAL_NUMBER_TY_Compare r1 r2; return UnsignedCompare(r1, r2); ];

#Endif; ! TARGET_GLULX